Operadores de fatorizacao na fisica matematica

Abstract

We present applications of factorization operators to solve linear second order differential equations as an alternativo to the Frobenius method in Mathematical Physics. In some simple examples, the factorization reduces a second order differential equation to a pair of first order differential equations, each one giving one of the linearly independent solutions. In other, generally eigenvalue equations, the factorization operators are identified with the eigenfunctions index raising and lowering operators; in these cases, one just need to solve the towest eigenvalue differential equations, where a simple integration is enough. We can also confirm that the majority of Mathematical Physics differential equations can be factored.